The dinosaurs would excist at the humans time if the asteroid hadn't had an impact... In other words, humans would have to adapt, as illustrated in the image above.
Edit:
Would've been so fucking awesome :/
Man put pimp hand down, on dino.
Man pull out gat, and buratdatdat.
[10:19] <~Tim> Why the fuck not, I'm insane :D
[12:06] <~Tim> Frost-Dragon: I bet you're sexy